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Paper detail

An optimal Liouville theorem for the porous medium equation

Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the heat equation. Additionally, for the homogeneous equation, we show that for the conclusion to hold, it is enough to assume the sharp asymptotic growth at infinity only in the space variable. The results are optimal, meaning that the growth condition at infinity cannot be weakened.

preprint2022arXivOpen access
Damião J. AraújoRafayel Teymurazyan
math.AP
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Damião J. AraújoRafayel Teymurazyan

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